// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/LU>

template<typename MatrixType>
void
determinant(const MatrixType& m)
{
	/* this test covers the following files:
	   Determinant.h
	*/
	Index size = m.rows();

	MatrixType m1(size, size), m2(size, size);
	m1.setRandom();
	m2.setRandom();
	typedef typename MatrixType::Scalar Scalar;
	Scalar x = internal::random<Scalar>();
	VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));
	VERIFY_IS_APPROX((m1 * m2).eval().determinant(), m1.determinant() * m2.determinant());
	if (size == 1)
		return;
	Index i = internal::random<Index>(0, size - 1);
	Index j;
	do {
		j = internal::random<Index>(0, size - 1);
	} while (j == i);
	m2 = m1;
	m2.row(i).swap(m2.row(j));
	VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
	m2 = m1;
	m2.col(i).swap(m2.col(j));
	VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
	VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());
	VERIFY_IS_APPROX(numext::conj(m2.determinant()), m2.adjoint().determinant());
	m2 = m1;
	m2.row(i) += x * m2.row(j);
	VERIFY_IS_APPROX(m2.determinant(), m1.determinant());
	m2 = m1;
	m2.row(i) *= x;
	VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);

	// check empty matrix
	VERIFY_IS_APPROX(m2.block(0, 0, 0, 0).determinant(), Scalar(1));
}

EIGEN_DECLARE_TEST(determinant)
{
	for (int i = 0; i < g_repeat; i++) {
		int s = 0;
		CALL_SUBTEST_1(determinant(Matrix<float, 1, 1>()));
		CALL_SUBTEST_2(determinant(Matrix<double, 2, 2>()));
		CALL_SUBTEST_3(determinant(Matrix<double, 3, 3>()));
		CALL_SUBTEST_4(determinant(Matrix<double, 4, 4>()));
		CALL_SUBTEST_5(determinant(Matrix<std::complex<double>, 10, 10>()));
		s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
		CALL_SUBTEST_6(determinant(MatrixXd(s, s)));
		TEST_SET_BUT_UNUSED_VARIABLE(s)
	}
}
